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A072742 Lesser members of a pair of primes (p, q) such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).

%I A072742 #29 Jan 22 2022 08:43:58
%S A072742 3,5,13,17,23,61,83,89,107,139,163,181,199,229,241,263,281,347,383,
%T A072742 431,461,467,503,577,601,619,727,751,757,769,811,877,919,997,1009,
%U A072742 1097,1187,1193,1217,1259,1277,1307,1319,1367,1409,1433,1439,1487,1553,1619,1637,1697,1787,1823,1889,1997,2027
%N A072742 Lesser members of a pair of primes (p, q) such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).
%C A072742 For each term p=a(n), the corresponding greater member is q=A072743(n).
%H A072742 Michel Marcus, <a href="/A072742/b072742.txt">Table of n, a(n) for n = 1..8217</a>
%e A072742    n  p = a(n)  q = A072743(n)   (p+q)/2
%e A072742   --  --------  --------------  ---------
%e A072742    1      3            5          4 = 2^2
%e A072742    2      5           11          8 = 2^3
%e A072742    3     13           19         16 = 2^4
%e A072742    4     17           47         32 = 2^5
%e A072742    5     23           41         32 = 2^5
%e A072742    6     61           67         64 = 2^6
%e A072742    7     83          173        128 = 2^7
%e A072742    8     89          167        128 = 2^7
%e A072742    9    107          149        128 = 2^7
%e A072742   10    139          373        256 = 2^8
%e A072742 As an irregular triangle, sequence begins:
%e A072742   [3],                             (k=2)
%e A072742   [5],                             (k=3)
%e A072742   [13],                            (k=4)
%e A072742   [17, 23],                        (k=5)
%e A072742   [61],                            (k=6)
%e A072742   [83, 89, 107],                   (k=7)
%e A072742   [139, 163, 181, 199, 229, 241],  (k=8)
%e A072742   ...
%o A072742 (PARI) listk(k) = {my(list = List()); forprime(p=2^(k-1)+1, 2^k, my(q=2^(k+1)-p); if ((q>p) && isprime(q), listput(list, p));); Vec(list);}
%o A072742 upto(k) = {my(list = List()); for (i=1, k, my(klist = listk(i)); if (#klist, for (j=1, #klist, listput(list, klist[j])));); Vec(list);}
%o A072742 upto(11) \\ _Michel Marcus_, Jan 22 2022
%Y A072742 Cf. A072743, A072744, A072745, A072746.
%K A072742 nonn,tabf
%O A072742 1,1
%A A072742 _Reinhard Zumkeller_, Jul 08 2002
%E A072742 Name corrected by _Jon E. Schoenfield_, Jun 27 2021
%E A072742 More terms from _Michel Marcus_, Jan 22 2022